The president has quite a bit of ability to set priorities and work assignments within the justice dept and intelligence agencies and other parts of the executive branch. Unlike legislative things, he really can just say “put 1,000 people on this Bin Laden thing” one day and just from that they just go off and do it exactly like he said.
Bush did pretty much the exact opposite, actively refusing to use his leadership position to instruct the people who worked for him to do anything about the threat that they were telling him existed. Idk if anything Gore did would have made a difference, but there definitely is a consensus that Bush fucked up on recognizing and reacting, in retrospect.